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 2020-09-13, 16:46 #12 RMLabrador     "Roman V. Makarchuk" Aug 2020 Ukraine 2×17 Posts I can explain why this test do not suffer for flaw of modulo computation.
 2020-09-13, 16:49 #13 RMLabrador     "Roman V. Makarchuk" Aug 2020 Ukraine 428 Posts I can explain why this test do not suffer modulo flaw.
2020-09-13, 17:05   #14
paulunderwood

Sep 2002
Database er0rr

3,533 Posts

Quote:
 Originally Posted by RMLabrador Attachment 23318 I can explain why this test do not suffer for flaw of modulo computation.
Code:
{forstep(n=9,77,2,
if(!ispseudoprime(n),
for(u=round(log(n)^2),n,
A=Mod(Mod([1+i,1;1,u],n),i^2+1);
X=A^n;
R=lift(lift(trace(X*i)))%i;
if(R==1||R==n-1,
print([n,u,R])))))}
[25, 11, 24]
[25, 12, 24]
[25, 16, 24]
[25, 17, 24]
[25, 21, 24]
[25, 22, 24]
[49, 15, 48]
[49, 21, 48]
[49, 22, 48]
[49, 28, 48]
[49, 29, 48]
[49, 35, 48]
[49, 36, 48]
[49, 42, 48]
[49, 43, 48]
[49, 49, 48]
[65, 20, 64]
[65, 22, 1]
[65, 30, 64]
[65, 33, 64]
[65, 41, 1]
[65, 43, 64]
[65, 59, 64]
[65, 61, 1]
[77, 25, 76]
[77, 44, 76]
[77, 58, 76]
You test works for some composites too.

Besides it makes no sense to use an inequality symbol when working with modular arithmetic.

Last fiddled with by paulunderwood on 2020-09-13 at 17:19

 2020-09-13, 17:23 #15 RMLabrador     "Roman V. Makarchuk" Aug 2020 Ukraine 2216 Posts ok. Key in the u value. Let them bigger! I'm put log^2 without deep thinking, there is some value, after all be ok. Just let u=1000000 and see result Believe me P/S Results are oscillating for the small u and for prime numbers go stable after some u For all other numbers for every u we got another result so if You found "exception" just test u+1 Last fiddled with by RMLabrador on 2020-09-13 at 17:36
 2020-09-13, 17:29 #16 paulunderwood     Sep 2002 Database er0rr 3,533 Posts That might take some time However: Code: {forstep(n=1001*1001,100000000,2, if(!ispseudoprime(n), for(u=1000000,n, A=Mod(Mod([1+i,1;1,u],n),i^2+1); X=A^n; R=lift(lift((trace(X*i))))%i;if(R==1||R==n-1, print([n,u,R]);break(2)))))} [1002001, 1000000, 1002000] You can play with this code by installing pari-gp if you have linux or by getting Pari/GP for windows at this site. Last fiddled with by paulunderwood on 2020-09-13 at 17:40
 2020-09-13, 17:39 #17 RMLabrador     "Roman V. Makarchuk" Aug 2020 Ukraine 2·17 Posts make test for u+1 for this case Thank You for the link! Last fiddled with by RMLabrador on 2020-09-13 at 17:58
 2020-09-15, 07:53 #18 RMLabrador     "Roman V. Makarchuk" Aug 2020 Ukraine 428 Posts At any rate, I am convinced that He [God] does not play dice./ Albert Einstein As mentioned, God do not play dice. Its true, I am convinced that He play Cards instead. /Roman V. Makarchuk Remember this. If we want to build skyscraper (of math) taller, we need good basement, isn't? Somebody know the rules of factors in numbers, their appearing, emerging, combination, I mean the RULES? We play the game in the blind state) For proof this simple test. we need to go deep below, to the kernel foundation, away of high grade construction, no matter how shiny wise or flying so mathematical high they are. test in this form still have probability nature, for every non prime number for any u chance of false exception 2/n where n is testing number. For u, u+1 - 4/n^2 and so on, for big numbers this goes to zero very fast. Repeated modulo operation erase the (easy) way to make the test deterministic, once again that arise form modulo computation. Just see the oscillation of result with only one modulo operation in the last step, you can do this for the small n~0-10000 P/S You may ask me about the proof.
2020-09-15, 09:06   #19
paulunderwood

Sep 2002
Database er0rr

3,533 Posts

Quote:
 Originally Posted by RMLabrador At any rate, I am convinced that He [God] does not play dice./ Albert Einstein As mentioned, God do not play dice. Its true, I am convinced that He play Cards instead. /Roman V. Makarchuk
Quote:
 God may not play dice with the universe, but something strange is going on with the prime numbers -- Paul Erdos

 2020-09-15, 09:49 #20 RMLabrador     "Roman V. Makarchuk" Aug 2020 Ukraine 2·17 Posts I'm one, who know. I'm reveal the part (of rules) and they resembling the card game) I can proof of this my claim for now, but just like recurrent sequence represent deferential equation, mention above will be represent of equation (of quantum mechanic) and above. So. if somebody wold like became the part of the history and have a some math level - you ale welcome. I have an unlimited amount of ideas, and, I suspect, no time. So, check this test first. or message me, and we discuss the proof of Riemann hypothesis - my ideas, your write in good English.
 2020-09-15, 10:39 #21 LaurV Romulan Interpreter     Jun 2011 Thailand 34·113 Posts The fact that god plays dice or not or she is scratching her ass (i mean donkey) is non sequitur. The test is just PRP in disguise.
 2020-09-15, 11:10 #22 RMLabrador     "Roman V. Makarchuk" Aug 2020 Ukraine 2·17 Posts Well, I'm explain why, not my fault if someone do not understand or do not at least check this out. This is my poor English. For the small u values, if we rise matrix to power without of modulo on the every step, and do it only one time, in the end, the result for prime and not prime numbers ARE deterministic, and, in general, is result of computing limitation or more precise, on the difference between analytical and numerical computation. if You look why this test work, you understand my point.

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